Recent developments in micro-electro-mechanical systems, also referred to as MEMS, have resulted in progressively more complex and capable MEMS components and has seen the incorporation and integration of such components, such as optics, micro-optics, microelectronics, micro-mechanics and semiconductor technologies into progressively more advanced micro-systems for a wide range of purposes and applications. A common need among such components systems, however, is the need to create optical structures, components and devices into or onto such MEMS devices and systems wherein such optical structures, components and devices involve and require the generation and implementation of intricate three-dimensional contours, optical radii and mathematically derived curves and diffractive or holographic structures.
The use of gray scale or gray tone techniques is advantageous in various imaging, printing, etching and machining processes used in creating MEMs components and systems and various optical devices or structures. These advantagous include, for example, the ability to form complex three-dimensional shapes into photo sensitive materials, specifically photo resists, as used in semiconductor manufacturing type processes. The formation of complex three-dimensional structures requires, however, a gray scale or gray tone photo mask or lithography mask which such masks have variations in transmission, either formed by stacking special coatings, etching the surface to selectively change the surface roughness or by changing the physical characteristics of the bulk mask material by electron beam writing. In all cases the methods are expensive and require specialized software processes, materials and techniques to generate the artwork or to process the mask blanks.
The fundamental theories and principles of gray scale or gray level images and processes have been clearly expressed in such publications as Gray Level Mask Theory (Prior Art) Wolfgang Henke, et al. Jpn J. Appl. Phys. Vol 33 (1994) pp. 6809–6815. Wolfgang Henke, et al, (1) illustrated the physical concept underlying gray level or gray tone concepts by describing how the projection imaging system of a wafer stepper acts as a spatial frequency filter. The amplitude in the image plane of the projection system is obtained from the mask amplitude transmission function T (x), which takes values of 0 or 1 behind opaque and transparent mask regions, respectively, in the following manner. The effect of a diffraction-limited optical system, i.e., no aberrations and no defocus, is to cut off higher spatial frequencies in the Fourier spectrum T′ (k) of T (x). T′ (k) and T (x) are related through the equations
                              T          ⁡                      (            x            )                          =                  ∫                                                    T                ′                            ⁡                              (                k                )                                      ·                                          exp                ⁡                                  (                  ikx                  )                                                            ⅆ                k                                                                        (        1        )            
                                          T            ′                    ⁡                      (            k            )                          =                              1                          2              ⁢              π                                ·                      ∫                                          T                ⁡                                  (                  x                  )                                            ·                                                exp                  ⁡                                      (                                          -                      ikx                                        )                                                                    ⅆ                  k                                                                                        (        2        )            The complex amplitude A (x′) in the image plane is given as
                              A          ⁡                      (                          x              ′                        )                          =                  ·                                    ∫                              -                k                            k                        ⁢                                          T                ⁡                                  (                  x                  )                                            ·                                                exp                  ⁡                                      (                                          -                      ikx                                        )                                                                    ⅆ                  ⅆ                                                                                        (        3        )            wherein k is a lateral wave vector component k=2π/λ sin θ=2πυ and where υ is the spatial frequency and wherein coordinates with primes refer to the image space. The maximum angle θc of the wave vector with the optical axis that may pass the optical system is given by the numerical aperture NA=sin θc, so the cut off frequency for a plane wave normally incident on the object, i.e., spatially coherent illumination, is given askc=NA2π/λ=2πυc.
If a one-dimensional grating is now used as an object having a pitch p, so that the ±1st and higher diffraction orders do not enter the entrance pupil of the optical system, the diffraction pattern in the pupil is given as a simple integral over the mask transmission function T (x) (eq. (2)). Hence, the intensity to be obtained in the aerial image is determined by the energy of the zero-th diffraction order. If the grating is a regular one, i.e., consisting of equal lines and spaces, T′(k=0)=0.5 and the aerial image intensity is I(x′)=A(x′)2=0.25. If one defines 1 as being the width of the Cr lines on a conventional quartz/Cr reticle, the parameter
                    B        =                  l          p                                    (        4        )            which can be termed as the filling factor of the reticle, describes the percentage of the total reticle area covered by opaque mask features, and determines the image intensity level l′.I′=(1−B)   (5)
Thus, by adjusting parameter B appropriately, arbitrary image intensity levels can be set, which can subsequently be used to mold a photosensitive resist layer. In standard wafer steppers the reticle is usually illuminated with partially coherent light. If the coherence parameter σ describes the size of the spatial coherence area on the reticle, the limiting spatial frequency passing through the stepper lens is given by
                              V          c                =                              (                          1              +              σ                        )                    ⁢                      NA            λ                                              (        6        )            Hence the limiting pitch is
                              p          c                =                              1                          1              +              σ                                ⁢                      λ            NA                                              (        7        )            Thus, if the conditionp≧pc   (8)is satisfied, the grating can generally be used to print any desired gray level on the wafer.
However, at this point it becomes clear that the pitch variable can and does cause variations in intensity and it must be noted that the violation of condition (8) will lead to undesired oscillations in the image intensity distribution. In the paper by Wolfgang Henke, et al, the gray level or gray tone mask technique utilizes square or round features which are adjusted in size to vary the intensity based on the spatial frequency filtering method. The problem with this method is that the diffraction, specifically edge diffraction is along a linear edge, the sides of the square aperture and along the outer curve of the circular aperture. This linear diffraction creates dead zones where apertures side by side, interfere, creating intensity variations that cause ultimate feature resolution issues. These issues include waffling, steps or ripples, which are formed into the photo resist that is exposed, leading to undesired optical effects. Because, Wolfgang Henke, et al, does not follow a true gray tone style grid or sub-grid square aperture configuration, this technique is severely limited in the number of gray levels (0 to 255) that can be achieved, effectively reducing the smoothness of transitions between the apertures.
The commonly known method and applications of gray tone or gray scale imaging include various methods of digital halftoning, sometimes referred to as spatial dithering, where halftoning is in general the process by which a continuous-tone, gray-scale image is rendered using only binary-valued pixels and which typically provides or employs 0 to 255 gray scale levels. As is well known and understood, the underlying concept and purpose of digital halftoning is to provide a viewer of an image the illusion of viewing a continuous-tone image when, in fact, only black and white pixel values are used in the rendering. In all cases, these gray level or gray tone algorithms were developed to create an image for viewing by the human eye, and have specific attributes tailored towards this task.
One well known and standard visual image halftone or graytone/level method is dispersed-dot ordered dithering, which occurs when halftone dots, or pixels, are of a fixed size. Clustered-dot ordered dithering, in turn, simulates the variable-sized dots of halftone printing screens in rendering the image. The most noted advantages of ordered dither techniques, however, are speed of implementation and simplicity, while the primary disadvantage is that ordered dithering of all forms produces locally periodic patterns in the halftoned image, which are visually objectionable to the human eye.
Halftoning gray tone/level methods using error diffusion algorithms, as first introduced by Floyd and Steinberg, are currently the most popular halftone image method used in the printing industry. Such methods, however, require neighborhood operations on the image, that is, the sampling of nearby pixels when evaluating each primary pixel. In this algorithm, the error of the quantization process is computed and spatially redistributed within a local neighborhood in an effort to influence pixel quantization decisions within that neighborhood and thereby improve the overall quality of the halftoned image. Once again, this method is primarily designed and adapted for visual impact to the human eye.
The classical approach to error diffusion for the formation of a gray tone/level mask, however, suffers from critical implementation constraints. In this case, the algorithm raster scans the image and, for each individual pixel, a binary quantization decision is made based on the intensity of the individual pixel and the weighted error from pixels within a predefined diffusion region of previously processed pixels. As a result, the diffusion filter is necessarily causal, resulting in undesirable intensity artifacts that will adversely effect the exposure of photo resist if used for gray scale exposure imaging using an optical lithographic technique.
In this regard, one conventional technique for forming a refractive element includes forming structures in photo-resist by patterning and melting a photo-resist layer on a glass substrate, the melting of the photo-resist resulting in the generation of spherical surfaces. An example of this technique is disclosed, for example, in an article by O. Wada, “Ion-Beam Etching of InP and it's Application to the Fabrication of High Radiance InGAsP/lnP Light Emitting Diodes”, General Electric Chemical Society, Solid State Science and Technology, Vol. 131, No. 10, October, 1984, pp. 2373–2380. However, this technique is limited to special shapes and can only provide spherical contours using a small positive photo resist layer. In addition, the refractive elements are produced by ion milling of the resist structure and the glass substrate wherein the ions first mill the resist and then, once the resist is removed in a certain region, mill the glass substrate, thereby transferring the resist structure to the glass substrate and thereby forming the refractive element.
A varied exposure pattern in a photo-resist can also be generated by directly exposing the photo-resist with a raster-scanned laser or electron beam. However, no mask is created in this method, and each element must be written one at a time, with no benefit of economies of scale. As is well understood, It is desirable to create a gray scale mask that can be reused multiple, for example, thousands, of times to make thousands of wafers.
An exposure mask for fabricating micro-lenses was developed and disclosed, for example, in U.S. Pat. Nos. 5,480,764 and 5,482,800 to Gal et al. and in an article by W. W. Anderson et al. “Fabrication of Micro-optical Devices” Conference on Binary Optics, 1993, pp. 255–269, in an attempt to overcome these limitations. According to the described technique, known as half-toning, the mask is created by constructing a plurality of precisely located and sized openings wherein the frequency and size of these openings produce the desired gray scale effect. However, the apertures of the method as described utilize a grayscale pixelized matrix format wherein the apertures follow a strict square aperture protocol using a pixel grid matrix and a sub-pixel grid matrix. As a consequence, this method leads to photo resist exposure variations that are highly undesirable for precise micro optic applications. In addition, and although this method can be considered halftoning, it is not true digital halftoning, which translates the grid style pixel format of a grayscale map generated by a software package and translates it into a true digital halftone or gray tone/level where an array of fixed sized dots are used to form clusters which relate to the intensity variations desired for the optimum human eye visual effect.
It must also be noted that in addition to the strict fabrication requirements for such masks, the masks are used with a stepper and, for this reason, the pattern of the mask is effectively reduced in size when the resist layer is exposed. This reduction is required because the gray scale resolution elements are binary in value and therefore must be blurred in order to present the desired gray scale effect, so that the gray scale resolution elements no longer appear to be distinct holes. This in turn requires that the mask be a number of times larger than the actual element and the mask will soon become impracticably large when attempting to simultaneously producing many elements. Also, steppers are very expensive equipment.
In addition, and because of the required reduction, the point-spread function is larger than the image of the smallest opening in the mask. This blurring allows the mask to form a gray level pattern in the photo resist, but the large size of the point spread function results in a decreased resolution, which is undesirable.
The present invention provides a solution to these and related problems of the prior art.